z

y

x

Coordenadas genéricas

Equação da Superfície Esférica

Raio = r

C(x_C ,y_C ,z_C)

 \overline{ AB } = \sqrt{(x_A-x_B)^2+(y_A-y_B)^2}

P(x, y)

Distância

Equação

\overline{ PC } = \sqrt{(x- x_C)^2+(y- y_C)^2+(z-z_C)^2}

 \overline{ PC }  = r

\sqrt{(x-x_C)^2+(y-y_C)^2 + (z-z_C)^2}  = r

(x-x_C)^2+(y-y_C)^2 + (z-z_C)^2  = r^2

x_C

y_C

z_C

O = (-0.6733740360669992, 0.33332563737207965)
a_1 = Line(O, yAxis)
b_1 = Line(O, xAxis)
A_1 = Point(b_1)
B_1 = Rotate(A_1, 45°, O)
α = Angle(A_1, O, B_1)
c = Line(O, B_1)
A = Point(c)
d = Line(A, b_1)
B = Point(b_1)
e = Line(B, c)
E = Intersect(d, e)
f = Line(E, a_1)
C_1 = Point(a_1)
u = Vector(O, C_1)
C = Translate(E, u)
g = Segment(A, E)
h = Segment(E, B)
i = Segment(E, C)
L = Point(a_1)
u1 = Vector(O, L)
M = Point(a_1)
f1 = Segment(O, M)
N = Point(b_1)
g1 = Segment(O, N)
P = Point(b_1)
v1 = Vector(O, P)
Q = Point(c)
w1 = Vector(O, Q)
R = Point(c)
h1 = Segment(O, R)
y_A: x(B) - x(O)
z_A: y(C_1) - y(O)
x_A: -((x(A) - x(O))^(3) + (y(A) - y(O))^(3))^(1 / 3) 1.5
T5: x_A + ""
T6: y_A + ""
T11: y_A + ""
T12: z_A + ""
T13: "C(" + x_A + "," + y_A + "," + z_A + ")"
a = false
v = Vector(E, C)
D = Translate(A, v)
w = Vector(E, B)
F = Translate(C, w)
Raio = 2 (slider from 0 to 5, step 0.1)
k = Circle(C, Raio)
j = Line(C, g)
l = Line(C, h)
G = Intersect(k, f, 1)
I = Intersect(k, j, 1)
G' = Mirror(G, C)
I' = Mirror(I, C)
m = Segment(I, G)
J = Midpoint(m)
K = Midpoint(G, J)
S = Midpoint(J, I)
K' = Mirror(K, i)
K'_1 = Mirror(K, j)
p = Conic(K'_1, G', K', G, K)
S' = Mirror(S, j)
S'_1 = Mirror(S, i)
q = Conic(S', I, S, S'_1, I')
r_1 = Arc(q, 3.141592653589793, 0)
s = Arc(p, 0, 3.141592653589793)
text1: "Raio =" + Raio
text5: "\overline{ PC } = \sqrt{(x-(" + x_A + "))^2+(y-(" + y_A + "))^2+(z-(" + z_A + "))^2}"
text6: "\overline{ PC } = " + Raio
text7: "\sqrt{(x-(" + x_A + "))^2+(y-(" + y_A + "))^2 + (z-(" + z_A + "))^2}  = " + Raio
text8: "(x-(" + x_A + "))^2+(y-(" + y_A + "))^2 + (z-(" + z_A + "))^2 =" + Raio + "^2"
b = false
o = false
H = Point(k)
r = Segment(C, H)